Shaping attraction basins in neural networks

Venkatesh, Santosh S.; Pancha, Girish; Sirat, Gabriel Y.

doi:10.1016/0893-6080(90)90052-m

Cited by 13 publications

(2 citation statements)

References 15 publications

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“…The stability determined by this algorithm is (11) The difference between the MOA and the PLR is that among the patterns that do not satisfy the separation condition ( for MOA and for PLR), the former chooses the one that has the minimum overlap (10) instead of updating sequentially as in (6). Krauth and Mézard proved that the MOA would stop in a finite number of iteration steps if the prototype vectors were linearly separable (at the th neuron ) and that for the stability would be maximized.…”

Section: B Minimum Overlap Algorithm (Moa)mentioning

confidence: 99%

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Designing Asymmetric Hopfield-Type Associative Memory With Higher Order Hamming Stability

Lee

Chuang

2005

IEEE Trans. Neural Netw.

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The problem of optimal asymmetric Hopfield-type associative memory (HAM) design based on perceptron-type learning algorithms is considered. It is found that most of the existing methods considered the design problem as either 1) finding optimal hyperplanes according to normal distance from the prototype vectors to the hyperplane surface or 2) obtaining weight matrix W = [w(ij)] by solving a constraint optimization problem. In this paper, we show that since the state space of the HAM consists of only bipolar patterns, i.e., V = (v1, v2, . . ., vN)T E {-1, +1}N, the basins of attraction around each prototype (training) vector should be expanded by using Hamming distance measure. For this reason, in this paper, the design problem is considered from a different point of view. Our idea is to systematically increase the size of the training set according to the desired basin of attraction around each prototype vector. We name this concept the higher order Hamming stability and show that conventional minimum-overlap algorithm can be modified to incorporate this concept. Experimental results show that the recall capability as well as the number of spurious memories are all improved by using the proposed method. Moreover, it is well known that setting all self-connections wiiVi to zero has the effect of reducing the number of spurious memories in state space. From the experimental results, we find that the basin width around each prototype vector can be enlarged by allowing nonzero diagonal elements on learning of the weight matrix W. If the magnitude of w(ii) is small for all i, then the condition w(ii) = OVi can be relaxed without seriously affecting the number of spurious memories in the state space. Therefore, the method proposed in this paper can be used to increase the basin width around each prototype vector with the cost of slightly increasing the number of spurious memories in the state space.

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Section: B Minimum Overlap Algorithm (Moa)mentioning

confidence: 99%

“…Some of them assume to be symmetric (e.g., [10], [11], [14], [15], [19], and [20]) whereas others allow to be asymmetric (e.g., [13], [15], [16], [18], and [20]). The advantage of using a symmetric is the absence of oscillation memories.…”

Section: Introductionmentioning

confidence: 99%